科研之友
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摘要
We show that a family F of analytic functions in the unit disk D all of whose zeros have multiplicity at least k and which satisfy a condition of the form %26lt;br%26gt;f(n)(z)f((k))(xz) not equal 1 %26lt;br%26gt;for all z is an element of D and f is an element of F (where n %26gt;= 3, k %26gt;= 1 and 0%26lt;|x|%26lt;= 1) is normal at the origin. The proof relies on a modification of Nevanlinna theory in combination with the Zalcman-Pang rescaling method. Furthermore we prove the corresponding Picard-type theorem for entire functions and some generalizations.
- 出版日期2012-4
